#arithmetization

14.1 Arithmetization

14.1 Arithmetization of Syntax Gödel’s key idea is that syntax can be represented inside arithmetic. Symbols, formulas, and proofs are encoded as natural numbers. Once this is done, statements about formulas become statements about numbers, and a formal system can reason about its own expressions. Coding Symbols Start with a finite alphabet of symbols: $$ {0, S, +, \times, =, (, ), \forall, \exists, \neg, \land, \lor, \to, \dots} $$...